mlsanityData to 14 Oct 2026

Fork Where the Model Changes Its Mind: Belief-Shift Branching for Tree-Structured Reinforcement Learning

arXiv 2609.11061 ↗First posted 10 Sep 2026cs.AIcited by 0

On the map: Deep reinforcement learning methods → RL training of language and agent models

Abstract (arXiv)

Tree-structured rollouts give critic-free reinforcement learning with verifiable rewards (RLVR) step-level credit: fork a chain at an intermediate point, and sibling outcome differences estimate step value. Each fork adds sampling cost, so realistic budgets typically allow only a few forks per chain. A fork placed where the outcome is already largely settled yields siblings that mostly agree and provide almost no credit signal; hence, for a given tree size, where forks are placed largely determines how much step-level RL can gain. Most existing mainstream methods place forks by structure, such as fixed lengths, midpoints, and delimiters, or by next-token entropy. We formalize fork placement as locating the pivots of the chain's value curve, where the expected outcome turns. We propose belief-shift branching: read the model's answer belief at candidate boundaries and fork just before the step where consecutive beliefs diverge most. Three instantiations, none needing step-level supervision, span access levels: a black-box probe, a logit-lens depth profile, and a learned activation direction, which is fit offline and therefore used only in the validation before RL training. The signal only places forks, and the probe costs about 1% of step compute on mathematics and under 5% on code when it runs inside the rollout engine. In that validation, against Monte-Carlo value curves, a belief-shift signal ranks first in each of the eight model×benchmark panels, ahead of entropy, structural, and LLM-judge baselines. In RL across three model families and two domains, belief-shift forking leads every mathematics aggregate, on OLMo-3-7B by +2.6 aggregate and +2.9 on AIME 2026 over the strongest baseline, and sweeps every OLMo code column, by +6.5 on LiveCodeBench-medium.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Placed in RL training of language and agent models, one of 15 directions in Deep reinforcement learning methods. Builds on 37 of its 71 references that are in the map. First posted on arXiv 10 Sep 2026.

Builds on

37 of 71 references.

References · 37

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25 more
  1. 2022Solving math word problems with process- and outcome-based feedbackcited by 901
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